I make a brief remark on the specification of the parametric trial assignment model in Equation REF . This does not necessarily need to be correct as long as it balances all the covariates, and potential transformations of these covariates, e.g. polynomial transformations and product terms, that modify the marginal treatment effect for \(A\)  vs. \(C\)  [1]}, [2]}. Squared terms are often included to balance variances for continuous covariates [3]} but initial simulation studies do not report performance benefits [4]}, [5]}. This is probably due to greater reductions in ESS and precision [6]}.
